Q. 7.28 - Elementary Statistics

Question

Does the sample size have an effect on the mean of all possible sample means? Explain your answer. 

Step-by-Step Solution

Answer

No, the sample size does not have an effect on the mean of all possible sample means. 

Step 1. Given Information

We need to identify whether the sample size has an effect on the mean of all possible sample means.

Step 2. Explanation

For any sample size, the mean of all possible sample means equals the population mean.

For samples of size n, the mean of the variable $\overline{x}$ equals the mean of the variable under consideration. That is, ${\mu }_{\overline{x}}=\mu$.

So, for every sample size, the sample mean is equal to the population mean and it does not depend on the sample size.

As a result, the sample size does not have an effect on the mean of all possible sample means.